The cross product, also called the vector product, is an
operation on two vectors. The cross product of two vectors produces a third
vector which is perpendicular to the plane in which the first two lie.
That is, for the cross of two vectors, A and B, we place
A and B so that their tails are at a common point. Then,
their cross product, A x B, gives a third vector, say C,
whose tail is also at the same point as those of A and B.
The vector C points in a direction perpendicular (or normal) to
both A and B. The direction of C depends on the Right
Hand Rule.

If we let the angle between A and B be ,
then the cross product of A and B can be expressed as

A x B = A B sin()

Figure 1A x B = C

If the components for vectors A and B are
known, then we can express the components of their cross product, C
= A x B in the following way

Cx = AyBz
- AzByCy = AzBx
- AxBzCz = AxBy
- AyBx

Further, if you are familiar with determinants, A x B, is

Comparing Figures 1 and 2, we notice that

A x B = - B x A

A very nice simulation which allows you to investigate the properties
of the cross product is available by clicking HERE.
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